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The Galen A. Foresman, Peter S. Fosl, and Jamie Carlin Watson CRITICAL THINKING THE CRITICAL THINKING TOOLKIT GALEN A. FORESMAN, PETER S. FOSL, AND JAMIE C. WATSON THE CRITICAL THINKING TOOLKIT This edition first published 2017 © 2017 John Wiley & Sons, Inc. Registered Office John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, UK Editorial Offices 350 Main Street, Malden, MA 02148-5020, USA 9600 Garsington Road, Oxford, OX4 2DQ, UK The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, UK For details of our global editorial offices, for customer services, and for information about how to apply for permission to reuse the copyright material in this book please see our website at www.wiley.com/wiley-blackwell. The right of Galen A. Foresman, Peter S. Fosl, and Jamie C. Watson to be identified as the authors of this work has been asserted in accordance with the UK Copyright, Designs and Patents Act 1988. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by the UK Copyright, Designs and Patents Act 1988, without the prior permission of the publisher. Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books. Designations used by companies to distinguish their products are often claimed as trademarks. All brand names and product names used in this book are trade names, service marks, trademarks or registered trademarks of their respective owners. The publisher is not associated with any product or vendor mentioned in this book. Limit of Liability/Disclaimer of Warranty: While the publisher and authors have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim a; ny implied warranties of merchantability or fitness for a particular purpose. It is sold on the understanding that the publisher is not engaged in rendering professional services and neither the publisher nor the author shall be liable for damages arising herefrom. If professional advice or other expert assistance is required, the services of a competent professional should be sought. Library of Congress Cataloging-in-Publication Data Names: Foresman, Galen A., author. Title: The critical thinking toolkit / Galen A. Foresman, Peter S. Fosl, and Jamie C. Watson. Description: Hoboken : Wiley, 2016. | Includes bibliographical references and index. Identifiers: LCCN 2016006532 (print) | LCCN 2016012956 (ebook) | ISBN 9780470659960 (cloth) | ISBN 9780470658697 (pbk.) | ISBN 9781118982020 (pdf) | ISBN 9781118981993 (epub) Subjects: LCSH: Reasoning. | Critical thinking. | Logic. Classification: LCC BC177 .F67 2016 (print) | LCC BC177 (ebook) | DDC 160–dc23 LC record available at http://lccn.loc.gov/2016006532 A catalogue record for this book is available from the British Library. Cover image: Getty/© Lisa Quarfoth Set in 10/12pt MinionPro by Aptara Inc., New Delhi, India 1 2017 To our students and to the Logos Contents Acknowledgments Introduction The Very Idea of Critical Thinking Critical thinking in the formal and empirical sciences Critical thinking, critical theory, and critical politics Critical thinking, finitude, and self-understanding Using this book 1 2 4 5 5 Basic Tools for Critical Thinking about Arguments 1.1 7 Claims Beliefs and opinions Simple and complex claims Truth functionality 1.2 Arguments Logic vs. eristics Arguments vs. explanations 1.3 Premises Enthymemes Identifying premises 1.4 Conclusions Argument structure Simple and complex arguments Identifying conclusions xv 8 9 10 11 12 12 13 14 14 16 16 16 17 More Tools for Critical Thinking about Arguments 2.1 19 Deductive and Inductive Arguments Deduction Induction 2.2 Conditional Claims Necessary and sufficient conditions Biconditional claims 20 21 22 23 25 viii CONTENTS 2.3 Classifying and Comparing Claims Comparing claims Classifying single claims 2.4 Claims and Definitions Lexical, stipulative, ostensive, and negative definition Extension and intension Generic similarities and specific differences Definiens and definiendum 2.5 The Critical Thinker’s “Two Step”: Validity and Soundness/ Cogency and Strength Structure before truth 26 28 29 30 30 31 31 32 33 Showing Invalidity by Counterexample 35 Tools for Deductive Reasoning with Categories 3.1 39 2.6 26 3.2 Thinking Categorically Types and tokens 39 Categorical Logic 40 Quality, quantity, and standard form Venn diagrams and the meaning of categorical claims Distribution and its implications Existential import 3.3 Translating English Claims to Standard Form Implicit quantifiers Individuals Getting the verb right Adverbials Trust your instincts A caveat 3.4 Formal Deduction with Categories: Immediate Inferences Equivalences Conversion Contraposition Obversion The Aristotelian and Boolean Squares of Opposition 3.5 Formal Deduction with Categories: Syllogisms Categorical syllogisms Major and minor terms Mood and figure The Venn diagram test for validity Five easy rules for evaluating categorical syllogisms Gensler star test Tools for Deductive Reasoning with Claims 4.1 Propositional vs. Categorical Logics Translating claims into propositional logic 40 42 44 45 46 46 47 47 48 50 50 50 51 52 53 56 58 63 64 64 65 66 69 70 72 73 CONTENTS Truth tables for claims Testing for validity and invalidity with truth tables Indirect truth tables Strange validity 4.2 Common Deductively Valid Forms Modus ponens Modus tollens Hypothetical syllogism Disjunctive syllogism Constructive and destructive dilemmas 4.3 Equivalences Double negation Tautology Commutativity Associativity Transposition Material implication Material equivalence Exportation Distribution DeMorgan’s Law 4.4 Formal Deduction with Forms and Equivalences Three simple rules 4.5 Common Formal Fallacies ix 76 78 79 82 83 83 84 86 86 87 90 90 91 91 92 92 93 93 94 95 95 96 97 101 Affirming the consequent Denying the antecedent Affirming a disjunct 101 103 104 Tools for Detecting Informal Fallacies 5.1 Critical Thinking, Critical Deceiving, and the “Two Step” 5.2 Subjectivist Fallacy 5.3 Genetic Fallacies 5.4 Ad Hominem Fallacies: Direct, Circumstantial, and Tu Quoque 107 109 112 113 Direct Circumstantial Tu quoque 5.5 Appeal to Emotions or Appeal to the Heart (argumentum ad passiones) Appeal to pity (argumentum ad misericordiam) Appeal to fear (argumentum ad metum) Appeal to guilt 5.6 Appeal to Force (argumentum ad baculum) 5.7 Appeal to Ignorance (argumentum ad ignorantiam) Negative evidence and no evidence 5.8 Appeal to Novelty (argumentum ad novitatem) 114 115 118 120 120 122 122 124 125 126 127 x CONTENTS 5.9 Appeal to the People (argumentum ad populum) Bandwagon Appeal to snobbery Appeal to vanity 5.10 Appeal to Unqualified Authority (argumentum ad verecundiam) 5.11 Fallacy of Accident 5.12 False Dilemma 5.13 Semantic and Syntactic Fallacies Ambiguity, two types: lexical and syntactic Vagueness vs. ambiguity Vagueness, two types: degree and context Equivocation and fallacious amphiboly 5.14 5.15 5.16 5.17 5.18 5.19 5.20 5.21 5.22 5.23 5.24 5.25 Begging the Question (petitio principii) Question-Begging Sentences Missing the Point (ignoratio elenchi) Fallacy of Composition Fallacy of Division Is-Ought Fallacy Appeal to Tradition Quoting Out of Context Red Herring Straw Man and Fidelity Hasty Fallacization A Brief Argument Clinic Context Charity Productivity Tools for Critical Thinking about Induction 6.1 Inductive vs. Deductive Arguments Again 6.2 Analogies and Arguments from Analogy Criticizing analogies 6.3 Fallacies about Causation Post hoc ergo propter hoc Correlation is not always causation Cum hoc ergo propter hoc Neglecting a common cause Oversimplified and contributing causes Proximate, remote, and intervening causes 6.4 Inductive Statistical Reasoning Sampling: random and biased Stratification The gambler’s fallacy Averages: mean, median, and mode Distributions 128 128 129 129 132 135 137 138 138 139 139 140 143 144 145 146 148 149 152 153 158 159 161 162 162 162 163 166 167 168 170 170 171 172 172 174 175 177 177 178 179 179 180 CONTENTS 6.5 Base Rate Fallacy 6.6 Slippery Slope and Reductio ad Absurdum 6.7 Hasty Generalization 6.8 Mill’s Five Methods 1. Method of Concomitant Variation 2. Method of Agreement 3. Method of Difference 4. Joint Method of Agreement and Difference 5. Method of Residues Tools for Critical Thinking about Experience and Error 7.1 Error Theory 7.2 Cognitive Errors Perceptual error Memory Stress and trauma Projection Transference Confirmation bias Denial A little bit of knowledge … The fallacy of false consensus Naïve realism 7.3 Environment and Error 182 184 188 189 189 190 191 191 192 195 197 197 199 201 202 203 203 204 204 205 205 206 Obstruction and distraction Duration Motion Distance Context and comparison Availability error 206 207 207 207 208 208 7.4 Background and Ignorance 7.5 Misleading Language 209 210 Suspect the negative Implications and connotations Damning by silence or understatement 7.6 xi Standpoint and Disagreement 210 210 211 211 The mosaic of truth Incommensurability and deep disagreement 213 213 Tools for Critical Thinking about Justification 8.1 215 Knowledge: The Basics Ordinary belief and hinge propositions Plato’s definition of knowledge Chisholm and belief 216 216 217 xii CONTENTS 8.2 Feelings as Evidence Some important features of all types of feelings The importance of distinguishing sense experience from emotion 8.3 Skepticism and Sensory Experience The weaknesses of sense experience as evidence The strengths of sense experience as evidence 8.4 Emotions and Evidence The weaknesses of emotional experience as evidence The strengths of emotional experience as evidence Tips for eliminating the negative effects of emotions 8.5 Justifying Values The role of moral values in arguments Four common views of value judgment Tools for reasoning about moral values 8.6 Justification: The Basics Justification and the problem of access No reasons not to believe Beyond a reasonable doubt Obligation and permission to believe 8.7 Truth and Responsible Belief Why is responsibility relevant to belief? Responsibility without truth 8.8 How Does Justification Work? Claims as evidence Experience as evidence 8.9 A Problem for Responsible Belief Gettier cases Processes and probabilities as justification Varieties of externalism 8.10 Evidence: Weak and Strong Direct and indirect evidence Testimony as evidence Strong enough evidence? Suppressed evidence fallacy Four tips for recognizing “good” evidence 219 220 222 223 224 227 229 229 232 235 237 238 239 241 242 243 244 244 245 246 247 247 248 248 249 251 252 253 254 256 256 258 259 260 261 Justification: Conclusions 266 Tools for Critical Thinking about Science 8.11 9.1 Science and the Value of Scientific Reasoning Useful, durable, and pleasant goods An agreement engine A path to knowledge 9.2 The Purview of Science The limits of empiricism What is and what ought to be 271 271 272 272 273 274 274 CONTENTS Different kinds of science Critiques of science 9.3 Varieties of Possibility and Impossibility Logical possibility Physical possibility Other types of possibility 9.4 9.5 Scientific Method Experiments and Other Tests Six Criteria for Abduction Bad Science Tools from Rhetoric, Critical Theory, and Politics Meta-Narratives Stories that govern stories plus a whole lot more Governing, varying, and disintegrating narratives 10.2 283 289 Junk science Pseudo-science Fringe science Ideological science 10.1 281 281 282 Unfalsifiability and Falsification Resistance 1. Predictive power 2. Scope 3. Coherence with established fact 4. Repeatability 5. Simplicity 6. Fruitfulness 9.8 280 283 284 285 288 Controls and variables Epidemiological studies Personal experience and case studies Blinding and double blinding In vitro studies Non-human animal studies 9.7 275 279 Causal explanation Observation Verification and falsification Paradigms: normal and revolutionary science Ad hoc hypotheses and the fallacy of unfalsifiability Falsification and holism: hypothesis vs. theory The “no true Scotsman” fallacy 9.6 xiii Governing Tropes Simile, analogy, metaphor, and allegory Metonymy and synecdoche 10.3 The Medium Is the Message 10.4 Voice 290 291 291 293 293 294 295 296 297 297 298 299 299 300 300 300 301 302 302 302 303 303 305 305 306 308 308 309 311 313 xiv CONTENTS 10.5 10.6 Semiotics: Critically Reading Signs 316 Peirce and Saussure Of virgins, ghosts, and cuckolds The semiological problem 316 316 317 Deconstruction Critique of presence Undermining binaries The politics of deconstruction 10.7 10.8 Foucault’s Critique of Power The Frankfurt School: Culture Critique 326 Class Critiques Feminist and Gender Critiques Politics and gender Feminist critique Text and gender 10.11 Critiques of Race and Racism Scientific critique of race Liberal critique of race Marxist critique of race Critical race theory 10.12 Traditionalist and Historicist Critiques A history of thinking about history Views from nowhere The harm in forgetting The importance of careful listening 10.13 322 323 323 324 324 Classical Marxism: superstructure and substructure It’s the class hierarchy, stupid Exploitation, alienation, and class struggle False consciousness Criticizing class critique 10.10 320 320 321 Archeological method Genealogical method Microphysics of power and biopower Normalization Lipstick is ideology Makers who are made The Dialectic of Enlightenment 10.9 319 Ecological Critiques Consumption and pollution Ecological justice Non-human life Appendix: Recommended Web Sites Index 326 327 327 328 328 329 329 330 330 332 333 335 336 338 338 338 339 340 341 342 342 343 343 345 345 346 347 349 351 Acknowledgments The authors would like to thank in the first place our families for their patience as we labored on this book. Without their support, inspiration, and advice this project would not have come to fruition. In particular, we wish to thank Cate Fosl and Darlena Watson. We are especially grateful to Robert Arp for getting the ball rolling on this project, as well as to editors Jeff Dean and Liam Cooper for making sure it kept rolling. We thank Julian Baggini, too, for graciously permitting us to extend the Toolkit program to the field of critical thinking and for permitting us to rework material drawn from a number of entries in The Philosopher’s Toolkit for this text. We thank Nathan Gray and Nathan Eric Dickman (Young Harris College) as well as Robert Bass (University of North Carolina, Pembroke) for valuable insights and examples. We thank Kevin Decker for his close reading and helpful criticisms. One of the greatest critical thinkers we know, Jamie Miller, offered us helpful advice, pedagogical as well as logical. Cate Fosl (University of Louisville) offered important insights on matters of race and feminism. Jack Furlong and Bob Rosenberg (Transylvania University) helped refine sections dealing with the natural sciences. Alexander Dick (University of British Columbia) advised the authors on topics in critical theory. We are grateful, too, to the institutions that have supported our academic work: North Carolina Agricultural & Technical State University, Transylvania University, and Broward College. We are also grateful, more generally, for the continued existence of institutions of higher education that sustain the cultivation and communication of critical thinking. Our civilization depends deeply upon those efforts and on the support of donors, governments, and students. The professors who introduced us to logic and critical thinking deserve special acknowledgment, as we recognize that it is most immediately and perhaps most crucially through the efforts of fine teachers such as they are that good, clear, and critical thinking is cultivated in our world and passed on to new generations. Outstanding instruction in logic was afforded to us by Professor Frank Wilson at Bucknell University, by Burke Townsend at the University of Montana, Piers Rawling at Florida State University, and by Michael Bradie at Bowling Green State University. They in turn learned from fine and able teachers and inquirers into logic, epistemology, criticism, the sciences, and psychology in a weave of traditions that stretches back to antiquity. We hope in some small way to carry on xvi AC K N OW L E D G M E N T S those traditions in this volume. Any errors or shortcomings it presents are wholly our own. Wiley deserves our deep gratitude not only for publishing our work but also for advancing and sustaining thoughtful publications at a time when doing so is increasingly complex and difficult. No book produced through a fine publisher is realized without the guidance of its editors, and we have been especially fortunate in the editing provided by Alison Kostka, Liam Cooper, and Sally Cooper. We are grateful for the keen eyes and good judgment of copy editor Fiona Screen and proofreader Helen Kemp, for the talents of the artists who produced the book’s cover, as well as for the marketing and distribution teams that have made this text available to readers. We salute you all! Introduction The Very Idea of Critical Thinking Critical thinking sometimes seems as if it needs an apology, or rather it seems itself to be a kind of apology, an apology for the humanities and the liberal arts and sciences generally. Having failed to convince many people that the liberal arts are simply good in themselves or in their own terms, academics sometimes seem as though they have concocted the meretricious idea of “critical thinking” in order to help higher education sell itself to the worlds of commerce, law, and politics. Instead of arguing that the liberal arts comprise some of the very best ways to spend a human life, period (and that we ought, therefore, to support them enthusiastically and share them as widely as possible), academics seem inclined to wave the flag of critical thinking to convince governments, parents, students, and donors that the liberal arts offer something that’s “useful” or “profitable” in the “real” world. Critical thinking also seems to appeal to administrators and the administratively inclined because it poses as something testable, as composed of skills that produce “measurable outcomes” readily subject to “metrics” and “assessment.” Yielding measurable, quantifiable outcomes is important not only for demonstrating to those outside the academy the value of critical thinking and the liberal arts but also for “accountability,” for oversight, for ranking and managing, and perhaps for policing liberal arts faculties. There is truth in all this, embarrassingly so. But it’s not the whole story about critical thinking (or the liberal arts), not by a long shot. The authors of this book are convinced that the family of practices collected under the rubric of “critical thinking” does indeed include some of the best and most important activities human beings have forged and re-forged, shaped and refined over the last three millennia. It’s not too much to say, in our view, that critical thinking distills some of the very best of that inheritance. In the development of our sciences, our political institutions, and our very self-understandings, critical thinking has played a central role, and it’s simply The Critical Thinking Toolkit, First Edition. Galen A. Foresman, Peter S. Fosl, and Jamie C. Watson. © 2017 John Wiley & Sons, Inc. Published 2017 by John Wiley & Sons, Inc. 2 I N T RO D U C T I O N fine and good to pass on that treasure to future generations. What has been true of our history remains true today: strong critical thinking is not only useful for commerce, the law, and technology, it’s absolutely crucial to a dynamic and thriving culture, and it defines an essential component of any solid education. But what is critical thinking? What composes it? In this volume, we’ve taken a broad, interdisciplinary, and relatively comprehensive approach to critical thinking. While many critical thinking texts focus almost exclusively on logical topics, we’ve also compiled critical insights and practices that have been cultivated by the natural and social sciences, notably psychology, by literature and literary criticism as well as by the fine arts, and by political and social theories. We treat literature, rhetoric, and the arts not simply as obstructions or distractions that get in the way of clear, analytical, and logical thinking – though they sometimes can do that. We recognize in addition that the visual, literary, and generally rhetorical arts possess distinctive tools to enhance and deepen critical thinking. While the critical tools developed by philosophers, logicians, mathematicians, and empirical scientists are extremely important to good critical thinking, the critical instruments honed by theorists in literary, political, and social theory have been profound. No account of the possible methods of critical thinking available today would be respectable or even roughly complete without them. Arguments are, indeed, terribly important, but they’re not by any means the whole story of critical thinking. We encourage readers, therefore, to take a similarly broad, interdisciplinary, and inclusive approach and to consider the diverse ways critical thinking has been cultivated across the spectrum of reflective human thought. Critical thinking in the formal and empirical sciences Considering the structure of this book, we begin with logic, since logic is basic and essential to critical thinking. Chapters 1–4 of this ten-chapter volume are accordingly devoted to explaining some of the most important critical tools logicians have crafted, especially for the practices of what they call deductive reasoning. These techniques can seem a bit daunting to beginners, but because logic is so important we encourage you to press on through them. Logicians have studied the formal qualities of deductive inferences over thousands of years, and they’ve produced several logical systems that critical thinkers can use to test arguments. Those tests are not only indispensable tools for critical thinking. They also share the virtue of producing definite answers about good and bad reasoning using procedures that are clear, reliable, and not terribly difficult to use. The oldest of these systems we’ll address (Chapter 3) was systematized first by Aristotle in fourth-century bce Greece. It’s come to be called categorical logic since it’s a logic that’s based upon categories of things. We’ll map out seven tests for the validity of arguments using categorical logic. Those seven by themselves will provide critical thinkers with a rich and powerful set of tools to interpret and assess vast regions of human reasoning. I N T RO D U C T I O N 3 Yes, humans seem to possess a natural capacity for recognizing good reasoning even without studying critical thinking in a formal way, but the systems we present are important to master because they make it possible for skilled critical thinkers to build on that natural capacity and employ proven and useful rules in expansive ways – including articulating proper explanations and definitions, determining logical equivalences, and identifying contraries and contradictions, as well as a variety of other logical relationships. We’ll explain and demonstrate the use of helpful pictographic tests using Venn diagrams and Gensler stars, and after setting out some basic logical theory we’ll show you how to apply a number of simple procedures for reliably identifying valid and invalid arguments almost in a snap. The second principal kind of formal logic we’ll address (Chapter 4) has come to be called propositional or sentential logic – because, yes, it’s the logic of propositions or whole sentences. These sections will present you with additional ways to test arguments, especially through what logicians call truth tables, common forms of valid argument, and tried-and-true rules of inference. Truth tables are attractive to people because they offer a graphical way of testing arguments, and one that’s simplicity is perhaps even more exhaustive and direct than Venn diagrams. Learning the formal structures of the most common valid as well as invalid arguments together with what we think is an essential collection of other inference rules will help you sharpen the focus of your reasoning detectors so that the success or failure of arguments becomes much more easily recognizable. Chapter 5 sets out a substantial list of some of the most common ways people go wrong in their daily reasoning. These common informal fallacies aren’t failures of the formal or structural dimensions of arguments (the stuff of Chapters 3–4), but rather failures of another kind. Sometimes what goes wrong in reasoning isn’t a matter of argument form at all but instead often involves psychological factors that yield quasiinferences that pose as good reasoning but simply aren’t. Sometimes, alternatively, the problem lies with the underlying concepts and assumptions behind a claim. Those concepts and assumptions can be irrelevant, confused, or simply false, and as we’ll see they can really mess up your reasoning. Good critical thinking skills of the sort described in Chapter 5 have been designed to detect them, and there are many of them. Because some informal fallacies are particularly related to scientific thinking, we’ll broach additional informal fallacies across the remaining text, especially in those chapters devoted more directly to inductive reasoning and the empirical sciences. There are sadly, then, a lot of ways that reasoning can go wrong. The modern natural and social sciences were born from a struggle to deal with many of these kinds of error while simultaneously trying both to understand the world and to answer the philosophical challenge of skepticism – the idea that knowledge itself might not be possible. As a result of those challenges, scientists and philosophers of science developed important ideas regarding what counts in terms of empirical inquiry as good explanation and solid justification. We’ll therefore examine what makes scientific forms of inquiry so strong, and we’ll also look at how science can go wrong. Chapters 6–9 will draw lessons in critical thinking from the natural and social sciences as well as 4 I N T RO D U C T I O N from ongoing philosophical confrontations with skepticism. We’ll examine how best to confront the epistemological challenges of skepticism, how to think well and critically about causal explanations and statistical claims, how to enlist scientific principles critically, how to think critically even about science itself, and we’ll consider what science has learned about why human beings make errors. Critical thinkers should certainly be able to assess non-scientific claims using scientific rationality, but they should also possess some facility with assessing scientific claims themselves. Critical thinking, critical theory, and critical politics Human beings are linguistic beings. We communicate, reason, and criticize using language, and the critical theories developed by scholars in fields related to rhetoric, languages, and literature have gone a long way toward explaining not only how communication works but also how it fails to work – that is, how language and our human modes of expression themselves create, even require, the possibility of error, confusion, and misunderstanding. The meanings we wish to express are difficult to express. They’re elusive and fragile and complicated. We all know this on some level, but critical thinkers must become especially sensitive to it. Narratives, poetic tropes, voice, and other rhetorical dimensions of texts, however, not only offer opportunities for error and distortion. They also yield indispensable ways of understanding our selves and our world. Chapter 10 is designed therefore to help you consider critically the rhetorical and semiotic dimensions of the world in whatever text you confront – and not just in a theoretical way. Like our other chapters, Chapter 10 offers examples and problems for you to use in putting these tools to work. Human practices of expression are also tied up with political relations. We are, as Aristotle observed, political animals. Moreover, political theorists, especially across the past few centuries, have come to understand that politics doesn’t only exist in the halls of government, in voting booths, on explicitly political Internet web sites, or on clearly political TV or radio talk shows. Politics is, rather, pervasive and infuses our ordinary language, our concepts, our conduct, indeed the very institutions that compose our societies and cultures broadly speaking. Engaging political as well as moral topics critically, therefore, may involve not only thought but also action. Political action may be a matter of subversion and destabilization, of prising open spaces for new ways of life, and deconstructing what we determine needs to change. It may also, however, be about justifying and stabilizing values, principles, and moral claims – those that already exist and we think it important to keep, to protect, and to secure. In order for readers to engage their own political world more effectively, in addition to questions related to justification and values in Chapters 6–9 we also lay out tools drawn from political theory in Chapter 10. We don’t presume the political theories we describe to exhaust the field of political thought, and we don’t necessarily endorse them ourselves, but we do think these are among the most important critical approaches today, and it’s necessary for able critical thinkers to gain some facility with them. I N T RO D U C T I O N 5 Strong critical thinkers, in sum, should be able not only to wield the tools of logic and science but also those that illuminate the complexities of language and communication as well as those that help confront, advance, or resist the principal forms of morality and politics at work in the world today. Critical thinking should not only be directed toward improved inquiry into questions of truth and falsehood but also into issues of meaning more generally as well as imperatives and possibilities of moral and political action. Critical thinking, finitude, and self-understanding There’s something else. We wish to make it clear that critical thinking, like our book as a whole, is about self-understanding. It’s part of that ancient project enshrined in the inscription on the temple at Delphi and in the liberal arts and sciences: “know thyself.” Using critical thinking we produce critiques not just of arguments, data sets, propositions, and texts in the abstract. We also produce critiques that reveal our limits, our weaknesses, our finitude, and our selves as we actually exist in the world. Thinking about the world, about others, and about ourselves in light of a reflective and critical self-understanding of the human condition may be even more important than winning arguments or unreflectively accumulating facts, wealth, or power. It may, indeed, be the most important critical thinking outcome of all. Using this book This volume is not a complete text in logic, cognitive psychology, epistemology, critical theory, or political and social theory. The world of ideas is vast. We have collected what we think are the essentials for a basic grasp of critical thinking, and we have compressed, so far as possible, our entries to provide you with substantial and sophisticated but also concise accounts of the tools we address. You may read the text sequentially since it follows an arc from the positive establishment of claims through the complexities of logical and scientific thinking and reasoning to, finally, a critical denouement in rhetoric and politics. But the text may be read in other ways, too. You may start anywhere and either follow your own muses or fork off onto the network of paths we recommend using the suggested “See also” pointers at the close of most entries and chapters. You will often see us referring in the body of the text to the preceding toolkits in this series: The Philosopher’s Toolkit and The Ethics Toolkit. That’s because we understand these books to work together synergistically with ours, and they often offer entries that complement and enrich our own. Some of the entries of this volume overlap with entries in those other toolkits (and we are grateful to Julian Baggini for permission to do that), and so together we think they offer a kind of functional whole of critical and philosophical thinking. But this volume stands on its own, too, very much so; and it offers readers a fine gateway all its own to these powerful, critical tools. 6 I N T RO D U C T I O N Our book also contains larders of examples and problems for study and exercise. These may be enlisted by instructors in their class preparation or simply by readers for further reflection. As we’ve not always provided answers to these problems and questions, they’re as much matters of provocation as instruction. A list of web sites at the end of the volume suggests additional resources relevant to critical thinking freely available on the Internet. Know thyself and think critically. 1 Basic Tools for Critical Thinking about Arguments 1.1 Claims “Listen to reason!” cried Charlotte, exasperated after an hour of argument with Charles. And Charlotte’s frustration may have been perfectly justified. What is reason? And why should we listen to it? Most basically, reasoning is about advancing truth claims by means of special logical procedures of argument (see 1.2). One of the most basic elements of critical thinking, then, especially when engaged with issues related to logic and science, is to discern whether claims are actually true and to distinguish them from claims that are not true. In practice, language is our most fundamental tool in this process. Language allows us to articulate what we judge to be true or false, and it allows us to share and communicate those judgments to others. Ultimately, a good critical thinker must develop an acute grasp of language in order to make clear and precise claims about the truth and to assess how well or badly they function in the logic of an argument. Logicians have technical names for the kind of sentences out of which logical arguments are built. They call them statements or propositions, and they’re simply sentences that can be either true or false (in logical terms, they possess a truth value). To really understand statements and their truth values, however, keep the following in mind. r Bivalence. Statements or propositions can only have one truth value, and it must only be either true or false. Moreover, statements or propositions can’t be both true and false in the same sense under the same circumstances. Logicians call this the principle the law of bivalence. (To be sure, there are multi-valued logics with values besides true and false, but again they’re the subject of a different, more advanced book.) r Excluded middle. There’s no middle ground or gray area between truth values in basic logic – no “truthiness” as the comedian Steven Colbert might say. Statements or propositions can’t be “sort of true” and “sort of false.” Logicians call this The Critical Thinking Toolkit, First Edition. Galen A. Foresman, Peter S. Fosl, and Jamie C. Watson. © 2017 John Wiley & Sons, Inc. Published 2017 by John Wiley & Sons, Inc. 8 r B A S I C TO O L S F O R C R I T I C A L T H I N K I N G A B O U T A R G U M E N T S requirement the law of excluded middle. (Yep, there are fuzzy logics that accept gray areas, but we won’t be dealing with them here.) Non-statements and propositions. Keep in mind, too, that sentences that aren’t (in logic’s technical sense) statements or propositions simply don’t have truth value. Neither questions (“Where are you going?”) nor commands (“Stop that!”) nor exclamations (“Wow!!!”) are properly speaking true or false; and so they can’t be proper parts of arguments, logically understood. Now, the idea of a claim, in the sense we use the term here, adds for the sake of critical thinking just a bit more to what logicians strictly call statements and propositions. In particular, claims are statements that indicate a position has been taken. A claim, in other words, is a statement or proposition that in some meaningful sense sincerely belongs to whomever or whatever asserts it. One of the first judgments a good critical thinker must make, then, is to determine in just what way a statement is presented. Perhaps it’s meant sincerely and seriously, but perhaps it’s just being used hypothetically, ironically, as a joke, an instructive example, a lie, or perhaps in the recitation of some movie script. Or maybe it is simply being used to provoke an audience, to gain attention, to test someone’s response, or perhaps for some other reason entirely. There are countless things one can do with words and other forms of expression. So, while most of the material in this and the next four chapters applies to all claims, and not just to statements or propositions, we will use the language of “claims” to keep the question of claim or non-claim in mind. Here’s the upshot. Since it’s often the case that critical thinking involves discerning truth and error, a good critical thinker must learn how to identify claims that are true, or most likely seem true, while at the same time recognizing and avoiding claims that are best judged false. What’s more, a good critical thinker will recognize and admit when he or she does not know whether a claim is true or false. Critical thinking sometimes requires reserving judgment as to whether or not a claim is true until, if ever, sufficient reason for determining the truth or falsity of that claim is discovered. Beliefs and opinions In the 1989 comedy film, The Big Lebowski, a competitor scheduled to face the main character, the Dude, in the next round of a bowling tournament declares that his team is going to crush the Dude’s. The Dude, at least pretending to be unfazed, responds, now famously, by remarking, “Well, that’s just your opinion, man.” It’s not uncommon for people to distinguish strong truth claims from those that are weaker by calling the weaker claims opinions. People often make claims such as, “The world is round,” implying it’s something we definitely know to be true, that it’s a fact. When, on the other hand, people make claims such as, “Pele was a better athlete than Gretzky,” we deflate the claim by saying that it’s just their “opinion.” Beliefs can obviously often be either true or false, but a misleading though nevertheless common misunderstanding about the difference between strong assertions B A S I C TO O L S F O R C R I T I C A L T H I N K I N G A B O U T A R G U M E N T S 9 (such as knowledge claims) and mere opinions is that opinions aren’t really true or false. As such, they’re often thought to be free from the same scrutiny and justification required by claims to know. The result of this mistaken view is that many people believe that one’s opinions are somehow insulated from dispute or challenge. Opinions are treated as if they stand alone as islands in our thoughts, entirely disconnected from criticism and critical thinking. In reality, however, our opinions are still very much claims open to criticism. They are, after all, claims, and therefore either true or false. (Matters concerned with knowing are described as epistemic, and epistemology is the study of knowledge. Matters concerned with belief we’ll sometimes call doxastic.) In addition, it’s important to understand that opinions are often influenced by what we value. This mixing of beliefs and values sometimes makes it difficult or confusing to assess their truth. But a good critical thinker’s toolkit provides the tools for tackling this seemingly tricky task (see 5.5, 7.2, 8.2, and 8.5). In the meantime, just keep in mind that opinions often incorporate judgments and emotions about what is valuable, either subjectively, to the person expressing the opinion, or objectively, to everyone in the world. Simple and complex claims A simple claim is a claim that, logically speaking, isn’t divisible into other, more basic claims. This is usually a single subject-predicate formula, for example, “It is a cat,” or “That ball is round.” A complex or compound claim is a claim logically composed of two or more claims (or, minimally, a single claim that’s negated) connected by special words or ideas logicians call logical operators or connectives. (Of course, not all devices to connect one sentence with another do so as a matter of logic – as any poet or lyricist will tell you.) Simple claims, as some logicians have observed, are kind of like atoms, while complex claims are kind of like molecules. The claim that “Earth exists” is a simple claim. If, however, we add to the claim that the Earth exists another claim, “Humans live on Earth,” then we will have created the complex or molecular claim: “Earth exists, and humans live on it.” Notice that a complex claim may be expressed in lots of ways, and yet still be composed of the same simple claims: Humans live on Earth, and Earth exists. Humans live on Earth, which exists. Earth exists, and humans live on Earth. Sometimes, two sentences, whether simple or complex, can be said to possess the same meaning. Having the “same meaning” can, however, mean a variety of things. In this context, let’s just say that sentences having the same meaning can be used interchangeably, and one reason for this may be that the claims have the same cognitive or material content. (Another reason, as we’ll discover in the next three chapters, may be that they have the same formal qualities, which means they have the same logical 10 B A S I C TO O L S F O R C R I T I C A L T H I N K I N G A B O U T A R G U M E N T S structure.) The cognitive or material content of most claims determines the conditions that make those claims true or false – or what logicians call the truth conditions. In other words, the claim that the Earth exists is true if and only if the Earth really exists. The Earth’s existing is the condition that must be met in order for the claim “Earth exists” to be true. The truth conditions of complex claims, however, are a bit more, well, complex than those of simple claims. The truth conditions of complex claims are determined not only by the simple claims from which they are constructed but also by the logical operators or connectives used to combine the simple claims and sometimes other properties of the complex. Common logical operators are “and,” “or,” “if,” “if and only if,” and “not.” (The last of these, “not,” is unique and extremely powerful. It’s not used to combine multiple simple claims, but rather to change the truth value of a claim, whether simple or complex, to its opposite value. If true, a negated claim becomes false; if false, a negated claim becomes true.) Earth exists. Earth does not exist. Earth exists, and humans live on it. Earth exists, or humans live on it. Earth exists, if humans live on it. Earth exists, if and only if humans live on it. simple claim negation (not) conjunction (and) disjunction (or) conditional (if) biconditional (if and only if) Of course, each of these claims has a different meaning, and those meanings are derived from the cognitive content of the simple claims – “Earth exists” and “Humans live on it” – as well as from the logical operators that are used to combine or modify those simple claims. Here’s a tricky bit. It’s important to remember that despite the number of simple claims composing a complex claim, a complex claim can be viewed as one, big single claim. That’s because a complex claim is, as a whole, either true or false, just like a simple claim. The simple claims “Earth exists” and “Martians exist” have truth values (the first is true and the second, we presume, is false). But combine them into a complex claim using a connective and the result has its own truth value: the claim “Earth exists and Martians exist” is false; the claim “Earth exists or Martians exist” is true. You will see exactly why in Chapter 4. For now, just be aware that complex claims are single if not simple claims, and that each has its own single truth value. Truth functionality Here’s something even a little trickier. The truth value of different kinds of complex claims must be determined in different ways. For some complex claims, the truth or falsehood of the whole is completely determined in a logical sense just by the truth values of the component claims that compose it as well as by the way they relate to one another – that is, by (1) the simple claims plus (2) the logical operators that connect B A S I C TO O L S F O R C R I T I C A L T H I N K I N G A B O U T A R G U M E N T S 11 and modify them. For other kinds of claims, you can only determine the truth value of the whole claim by considering other features of the claim and perhaps only the claim as a whole. When the truth or falsehood of the whole is fully determined by the truth values of its component simple claims plus their logical relations (the first type), we call the claim a truth function or say that the sentence is truth functional. There are lots of other simple and complex statements and claims, however (the second type), that don’t possess this property. Belief statements, for example, are not truth functional. So, the truth value of the sentence, “Oedipus believes that the husband of Jocasta is not the killer of Laius,” does not, tragically for Oedipus, depend upon the truth or falsehood of its component simple claim, “the husband of Jocasta is the killer of Laius.” Unfortunately, whether or not we believe a statement is often independent of whether or not it’s true. (The distinction between truth functions and non-truth functions may seem a bit arcane at this point, but truth functionality will become especially important later, and we’ll elaborate on the concept a bit more when we address propositional logics in Chapter 4.) SEE ALSO 4.1 Propositional vs. Categorical Logics 8.1 Knowledge: The Basics 9.5 Unfalsifiability and Falsification Resistance READING Patrick J. Hurley, A Concise Introduction to Logic, 12th edn (2015), Sections 1.1, 2.2, 6.2 Julian Baggini & Peter S. Fosl, The Philosopher’s Toolkit (2010), Chapters 1–3 Anthony Weston, A Rulebook for Arguments, 4th edn (2009), I.1 J. van Benthem, A Manual of Intensional Logic (1988), Part I 1.2 Arguments A well-known Monty Python skit presents two men at an “Argument Clinic,” a client and a “professional” arguer. The fun begins when the professional arguer simply contradicts everything the client says (“Yes, I did.” “No, you didn’t.” “Yes, I did.” and so on.). Shrewdly, the client isn’t impressed: “Look this isn’t an argument … It’s just contradiction.” Okay, so what does count as an argument? For critical thinkers, the term “argument” means something very specific. Briefly put, an argument is a special tool that systematically collects and arranges reasons in support of the truth of a claim. As the client of Monty Python’s Argument Clinic 12 B A S I C TO O L S F O R C R I T I C A L T H I N K I N G A B O U T A R G U M E N T S puts it, “An argument’s a collected series of statements to establish a definite proposition!” A bit more specifically, arguments are simply sets of claims in which one or more claims are to provide support or justification or proof for the truth of another claim. Essential to every argument, then, are at least two components: (1) a single conclusion and (2) at least one reason or premise for the conclusion to be true. Identifying which is which in a given case can sometimes be confusing, though. That premises are intended somehow to support or seem to support a conclusion indicates that a third element is present in logical argument – (3) an inference from the premise(s) to the conclusion. It’s in the quality of that inference where things get especially interesting for critical thinkers, as not all inferences are good or strong or legitimate. Logic vs. eristics It’s common for people to confuse verbal altercations with arguments, since commonly, the term “argument” refers only to a dispute between two or more people, any kind of dispute. It’s also common for people to confuse eristics (the study of winning disputes) with logic (the study of reasoning). Arguments, however, in the technical, logical sense discussed here do not require a dispute, disagreement, or even dialogue, and they certainly don’t involve yelling, screaming, fisticuffs, or kerfuffles of any other sort. Furthermore, debates are also commonly confused with arguments because they are typically composed of many arguments, and the opposing sides of a debate offer arguments in support of the claims they wish to establish. So, debates include argument, but you needn’t have a debate to argue. Arguments vs. explanations Moreover, not all sets of sentences that lead to statements claimed to be true are arguments. For that reason, often a critical thinker will find himself or herself trying to determine whether or not a set of claims is, in fact, an argument. For example, explanations often seem like arguments. But there is deep difference between the two. Explanations are sets of claims that function to establish how or why something is the case. Arguments, in contrast, undertake to establish that some claim, normally a claim in question, is actually true. It’s very different, for example, to explain how extraterrestrials have made their way to Earth from arguing that extraterrestrials have made their way to Earth – though both might involve presenting a flying saucer. Arguments show that something is the case. Explanations show how or why something is the case. Explanations are easily mistaken for arguments because in many respects the two share stylistic similarities. Much like an argument, an explanation will include a single claim upon which all the other claims bear. In an explanation, this claim is called an B A S I C TO O L S F O R C R I T I C A L T H I N K I N G A B O U T A R G U M E N T S 13 explanandum, and the remaining claims, called the explanans, are used to account for (“explain”) the explanandum. Because an explanandum is a claim like any other, it is true or false. But an explanation is in no way concerned with establishing or supporting the truth of the explanandum. Instead, the truth of the explanandum is already accepted or presupposed. Often, explananda are easily identifiable because they’re not controversial, or we have no obvious reason to doubt that they are true. Take, for example, the following set of claims: The speed limit on this road is 45 mph, except when school is starting or ending, at which time it drops to 25 mph. That’s because during those times it’s especially important to protect the school children. The truth of the explanandum, “The speed limit on this road is 45 mph, except when school is starting or ending,” is not at issue. The explanans merely attempts to make clear why this is so. SEE ALSO 2.1 Deductive and Inductive Arguments 4.1 Propositional vs. Categorical Logics 6.2 Analogies and Arguments from Analogy READING Arthur Schopenhauer with A. C. Grayling, The Art of Always Being Right (2012/1831) Ernest Lepore & Sam Cumming, Meaning and Argument (2012) Miriam Joseph with Marguerite McGlinn, eds., The Trivium (2002) G. B. Kerferd, The Sophistic Movement (1981) Ernest Nagel, The Structure of Science: Problems in the Logic of Scientific Explanation (1979) 1.3 Premises One clear difference between proper argument and mere contradiction (as well as most shouting matches) is that an argument depends for its strength upon premises functioning as reasons to accept the conclusion. Premises give an argument its heft, its strength, the ground upon which the conclusion stands. They work together in exacting ways to prove or demonstrate or justify the conclusion. Some arguments enlist only one premise (and every argument must have at least one premise). That seems obvious, since there must be at least one reason to accept the conclusion in order for 14 B A S I C TO O L S F O R C R I T I C A L T H I N K I N G A B O U T A R G U M E N T S a set of claims to count as an argument. But that’s just the minimum. It may seem odd, but maximally there is no limit on the total number of premises an argument can enlist. An argument may indeed require volumes of text to complete, containing a staggering number of premises, perhaps (though this is something of a matter of dispute) even an uncountable or infinite number. Enthymemes Often, an argument will contain implicit or unspoken premises, usually probable claims already accepted by the audience. Arguments of this sort are called enthymemes. Enthymemes, then, are informal arguments that rely on premises not explicitly articulated. (We’ll see more of them in Chapter 3 when we consider Aristotelian or categorical arguments.) Since enthymemes are not uncommon, in order to assess the merits of arguments properly, a critical thinker will find it very helpful to look for enthymemes or enthymematic arguments and flush out their implicit or assumed claims. In short, sensitivity to enthymemes helps discern assumptions. Identifying premises Identifying the premises of an argument is made a lot easier by first identifying the argument’s conclusion. Once the conclusion is identified, any remaining claims that are there to support the truth of the conclusion become easier to discern. There are, however, several caveats of which critical thinkers should be mindful. First, it’s not necessarily the case that all of the claims in any given text are used as premises. Many texts contain lots of pieces of information that play no logical role at all in supporting the truth of the conclusion. For example, some claims merely elaborate, highlight, clarify, or give examples in relation to one of the premises. Some sentences are there just for rhetorical purposes. Sentences of those kinds are not relevant to the logic of the argument, though they may be used to clarify or explain a claim or a term, or they may be used to make the argument flow more smoothly. And so the critical thinker will find it useful to set these aside when analyzing and evaluating the argument. Second, as we’ve seen, claims may be complex. So critical thinkers will need to consider whether or not compound claims should be untangled and broken up. A complex claim may be easier to work with if it’s broken up into separate claims. But be careful if you do this, because sometimes breaking up a complex claim can change its meaning, especially if you lose the effect of the logical operators. Thankfully, good writers often set off premises and conclusions with indicators. Indicators are either single words or phrases that alert the reader or listener to the logic of an argument. (It’s good, for that reason, to use logical indicators while writing or speaking. Your audience will thank you.) While it isn’t necessary for an argument to contain these words, they do help to clarify an argument’s structure. Words or phrases B A S I C TO O L S F O R C R I T I C A L T H I N K I N G A B O U T A R G U M E N T S 15 that are specifically useful to indicate that a premise precedes or follows the indicator word are called premise indicators. Here are some of the most common: since because given; given that for; for the reason that as; insofar as due to the fact that in that it may be concluded from For example: It will likely rain today given that it’s the rainy season and because the sky is full of thick, dark clouds. In this argument, two reasons are given for thinking it will likely rain today, and both are preceded by premise indicators: given that and because. Be careful, however, because some premise indicators perform other functions in our languages. The premise indicator word “since,” for example, does not always indicate that a premise is nearby, because “since” is also used to indicate that a period of time has passed. (“I’ve lived in this same house since 1965.”) Similarly, the word “because” may indicate a premise, but it may also indicate an explanans in an explanation (just as it does in the previous sentence, and also: “My house collapsed because of termite damage”). To be sure that the claim is a premise, a critical thinker must determine whether or not it functions as a reason to think another claim (the conclusion) is true. In an argument without indicators, a critical thinker must do this anyway, but the indicators make things easier by offering a shortcut to determining whether a given claim is best understood as a premise. These two formulations of the same argument demonstrate how the presence of indicators clarifies the relationship of the claims in an argument: 1. Riley is a mammal at the National Zoo. Riley is an elephant at the National Zoo. 2. Riley is a mammal at the National Zoo, given that Riley is an elephant at the National Zoo. In the first formulation of the argument, it is unclear whether the arguer is attempting to prove that Riley is a mammal at the National Zoo or instead perhaps just report that Riley is an elephant and a mammal at the zoo. Without the indicator words or phrases, readers can’t be sure how the text is being used. Context can help, but sometimes context is insufficient. The presence of the indicator phrase in the second formulation of the argument removes this complication by making it clear that one of the two claims is intended as a premise and the other as a conclusion. SEE ALSO 1.1 Claims 2.3 Classifying and Comparing Claims 3.4 Formal Deduction with Categories: Immediate Inferences 16 B A S I C TO O L S F O R C R I T I C A L T H I N K I N G A B O U T A R G U M E N T S READING Dan Cryan, Introducing Logic: A Graphic Guide (2004) Harry J. Gensler, Introduction to Logic (2010) Stan Baronett, Logic (2012) 1.4 Conclusions The conclusion of an argument is the claim that the premises are to support or justify. In large part, the conclusion is the main point of the argument. If an argument were like a treasure hunt, the conclusion would be the treasure, and the premises would be directions presented to get you to that destination. Similarly, every argument has one and only one conclusion. While there may be important points that must be made on the way to establishing a conclusion, ultimately all the important points should work together to support one single claim. Even though a single argument could take a book or more to complete, it would still have only one conclusion. Argument structure Now, authors do often claim to draw multiple conclusions from their arguments. Sometimes that means that they draw subconclusions on the way to a final conclusion. It’s also possible that the premises of the argument support the truth of multiple claims or a complex claim that can be broken into multiple claims. In even the terribly simple argument below, a single premise supports two different conclusions. P1. C1. C2. I have three buckets of apples. Therefore I have three buckets. Therefore I have apples. Given the premises provided, the author could have also concluded that he or she has material objects or simply something rather than nothing. When multiple conclusions can be drawn from a single set of premises, it is best to think of each conclusion as the result of a single argument. This is often the best practice because keeping arguments distinct, even when they share premises, can help prevent confusions that lead us to error. Simple and complex arguments Arguments come in all shapes and sizes. One way to describe the form of an argument is, as with premises, in terms of simple and complex. Complex arguments are B A S I C TO O L S F O R C R I T I C A L T H I N K I N G A B O U T A R G U M E N T S 17 arguments composed of two or more simple arguments. In a complex argument, the conclusions of simple component arguments become subconclusions in relation to the whole complex. As subconclusions in the complex argument, they also function as premises for the conclusion of the complex argument. Identifying conclusions As there are indicator words and phrases for premises, there are indicator words for conclusions as well. Conclusion indicators are words or phrases that alert the reader to the presence of the conclusion. Below is a list of commonly used conclusion indicator words and phrases: therefore it follows that; we may conclude that hence so; so that thus entails implies consequently Conclusion indicators are fairly reliable indicators of conclusions; but just as it was with premise indicators, it’s always important to check the claim indicated by the conclusion indicator to see if that claim is, in fact, the logical, final conclusion of the argument. It is not uncommon for conclusion indicators to mark the presence of a subconclusion in a complex argument. Context and the rules of logic will often clarify things, but it’s notoriously difficult, especially in highly complex texts, to discern the arguments. In fact, when we get to Chapter 10 (especially in 10.5), to what’s called the “semiological problem,” we’ll see that the very nature of language and interpretation ensures that this work remains difficult. That difficulty, indeed, is one of the reasons academic philosophers and other scholars remain in business! Exercises and study questions 1. 2. Determine whether the following claims are simple or complex: r Monday Night Football is the most widely watched television program in the United States. r If you go to the store, then please purchase some milk and eggs. r All the cars are vehicles with bad gasoline mileage. r Either the weather is going to improve, or we’ll need to cancel the picnic. Identify the premises and conclusion in the following arguments: r It’s important that we respect the choices of others, and it’s important that we help look out for the welfare of others. Consequently, we must ensure that the available choices for others are always ones that will benefit their welfare. 18 3. 4. B A S I C TO O L S F O R C R I T I C A L T H I N K I N G A B O U T A R G U M E N T S r The average age of cars on the road today is around 10 years. Since my car isn’t going to last much more than 7 years, its construction is probably inferior to most cars on the road today. r Most students haven’t discovered what they want to do with their lives, and yet many schools want them to declare a major before setting foot on campus. It follows from this that a student’s major should be lenient and flexible with the number of required courses, because inevitably students will take classes in a degree field that they may change after a short time. How many conclusions can an argument have? How many premises can an argument have? SEE ALSO 3.4 Formal Deduction with Categories: Immediate Inferences 3.5 Formal Deduction with Categories: Syllogisms 4.2 Common Deductively Valid Forms 8.6 Justification: The Basics READING Merrilee H. Salmon, Introduction to Logic and Critical Thinking (2012) Paul Herrick, Introduction to Logic (2012) Anthony Weston, A Rulebook for Arguments (2009) 2 More Tools for Critical Thinking about Arguments 2.1 Deductive and Inductive Arguments Bridges function properly when they are engineered with (a) strong materials and (b) a supportive structure capable of carrying the loads trucked across them. Arguments, curiously, function in a similar way. It’s just that the material out of which arguments are built isn’t concrete, steel, or stone. Instead, claims or statements function as materials for creating premises and a conclusion, and so the structure of arguments isn’t physical, but logical. Nevertheless, without the right materials and without having them assembled in the right way, an argument will fail just like a poorly built bridge. All arguments are intended to support the truth of their conclusions, but arguments can be structured in vastly different ways to achieve this goal. Similarly, two bridges built alternatively with concrete and steel may look and work in vastly different ways, like arch bridges and suspension bridges, for example. Regardless of their apparent differences, though, if they’re done right, if they have the right structure, they’ll still support a road along with the vehicles that drive over it. For arguments, it’s the logical structure that matters, and that structure determines the extent to which the argument will be what philosophers call truth preserving — that is, the degree to which reasoning from true premises ensures a true conclusion. It’s actually a pretty instructive term, since it captures something of the essence of what makes good arguments work, as well as the essence of what argument is about. In a good argument, true premises are worded and organized in a way that guarantees or makes it very likely that the conclusion is true; truth is preserved through the inference. Another way to think about this is to imagine that the truth of the premises in a good argument flows into the conclusion. The key to this amazing process (and this is important!) is the argument’s structure or form, and as such, assessing an argument’s form is a critical component for evaluating the overall success of the argument. The Critical Thinking Toolkit, First Edition. Galen A. Foresman, Peter S. Fosl, and Jamie C. Watson. © 2017 John Wiley & Sons, Inc. Published 2017 by John Wiley & Sons, Inc. 20 M O R E TO O L S F O R C R I T I C A L T H I N K I N G A B O U T A R G U M E N T S For this reason, arguments are categorized according to their forms and the extent to which they are truth preserving. Deduction Consider this: there are two ways an argument can be poorly engineered: (1) one or more of the premises – the materials out of which the argument is built – is false, or (2) the structure or form of the argument fails to provide adequate support for the conclusion. Of course, arguments whose forms, when functioning properly, are fully truth preserving are the strongest sort. They are called deductive arguments. When a deductive argument is properly structured, the argument is said to be deductively valid. When a deductively valid argument has true premises, it is called a deductively sound argument. In a deductively sound argument, the truth of the conclusion will necessarily follow from the truth of the premises. The idea has its roots at least as far back as Aristotle, who writes in the Prior Analytics (Prior Analytics; Book I, Chapter 2, 24b18–20), the fundamental text in the systematic study of deductive reasoning: A deduction is speech in which, certain things having been supposed, something different from those that are supposed results of necessity because of their being so. [Editors’ emphasis.] There is among philosophers, however, some controversy about what “necessarily” or “of necessity” means in the context of logic. So, one might say instead more cautiously that the conclusion of a valid deductive argument will “definitely follow,” “is sure to follow,” or “certainly follows.” That’s just to say, of course, that the truth of the conclusion is entirely supported through the argument’s structure and by the truth of the premises. Another common way to put this is to say that a properly structured deductive argument is constructed so that it is impossible for the conclusion to be false if the premises are true (if the premises aren’t all true, all bets are off). That impossibility is central to the way, as we’ll see, a lot of critical thinking about reasoning works. Of course, when an argument is not fully truth preserving, when the truth of the premises doesn’t entirely guarantee or ensure the truth of the conclusion, the argument is deductively invalid. Deductive reasoning is pervasive in the sciences and in our lives generally. Deductive arguments are common in mathematical reasoning, for example, and they are the kind of arguments that compose the core of computer programming. Generally speaking, however, the arguments people encounter are not usually formulated in the precise, deductively valid forms logicians prefer. Logicians clean things up, but not without some risk. While the practice of carefully recasting an argument so that it is clear and deductively valid can be extremely useful, there is some risk that the result won’t quite be relevant to what actually concerns people in a particular context. (We’ll address something of what logic can miss or lose when we address matters of rhetoric and poetics in Chapter 10.) M O R E TO O L S F O R C R I T I C A L T H I N K I N G A B O U T A R G U M E N T S 21 Induction There are many perfectly good arguments that aren’t deductive. These arguments do not guarantee their conclusions, but they do give them enough support that they should be taken seriously. Arguments that are not fully truth preserving but whose conclusions nevertheless follow with a degree of probability are what logicians call inductive arguments. The truth of the conclusion of an inductive argument always goes beyond the support of the premises to some extent, and so the extent to which the argument is truth preserving – its strength – depends upon the degree to which the premises support the conclusion. Inductively strong arguments are arguments structured such that the truth of the premises makes it very likely that the conclusion is true. Inductively weak arguments are arguments in which the truth of the premises does not lend much support to the conclusion. Of course, all this is a matter of degree, and so calling an inductive argument “weak” or “strong” may change with context. Normally, calling an inductive argument “weak” just means that, in terms of the case at hand, there is not enough support for the conclusion – in other words, that it would be unreasonable to accept the conclusion based solely on the premises. Most scientists engaged in inductive reasoning require a probability of 95% or more before accepting a conclusion as reasonable. The contexts of civil and criminal law, however, employ different standards of strength. In our dayto-day lives, a better than 50% chance of rain may be enough for us to conclude that we should carry an umbrella with us. Be careful, though. A deductive argument may contain premises that make probability claims yet still be a deductive argument. Remember that it’s not the content of the premises but the way they’re related to one another (their structure), the kind of inference they make, that determines whether or not an argument is best understood as deductive. For example, even though the following argument involves claims about what’s more or less probable, the structure of the argument is actually a well-established deductive form of inference called modus ponens (as we’ll see in 4.2): 1. If tomorrow’s game is a home game that will be played on a sunny day, then our team faces above-average chances of winning. 2. Tomorrow’s game is a home game that will be played on a sunny day. 3. Therefore, our team faces above-average chances of winning. While this may seem a bit confusing, here’s the point. When thinking critically about an argument, it’s often the case that, after identifying a conclusion and premises, the most pressing order of business is a bit of categorization, beginning with figuring out whether the argument is inductive or deductive. While this can prove tricky at first, as with most things it just requires some practice to get familiar with these categories. Ultimately, once the argument’s structure has been figured out, the proper criteria can be used in order to decide whether you’re dealing with a valid or invalid deductive argument or, instead, a strong or weak inductive argument. 22 M O R E TO O L S F O R C R I T I C A L T H I N K I N G A B O U T A R G U M E N T S SEE ALSO 1.2 1.4 6.1 Arguments Conclusions Inductive vs. Deductive Arguments Again READING Merrie Bergmann, James Moore, & Jack Nelson, The Logic Book (2013) David Papineau, Philosophical Devices: Proofs, Probabilities, Possibilities, and Sets (2012) W. V. O. Quine, Elementary Logic, revised edn (1980) Fred R. Berger, Studying Deductive Logic (1977) Aristotle, Prior Analytics (fourth century bce) 2.2 Conditional Claims When Sammy told her kids that, “If it rains, we’ll go to the movies,” she was making a conditional claim. A conditional claim is a type of complex claim in which the truth of one claim (the consequent) somehow depends upon or is contingent upon the truth of another claim (the antecedent). You might say that in a conditional claim, the consequent is true when the antecedent is true. Conditional claims are often articulated in the form “if p, then q,” where p and q can themselves be either simple or complex claims. For example, “If Barack Obama is president, then the United States has a Democratic president,” is a conditional claim composed of two simple claims: (1) Barack Obama is president, and (2) the United States has a Democratic president. In the common “if p, then q” form, p is the antecedent and q is the consequent, and so for the current example “Barack Obama is president” is the antecedent, while “the United States has a Democratic president” is the consequent. You may have noticed that our definition of “conditional claim” is broad. That’s intentionally so because for logicians there’s a pretty large range of what “depends upon” or is “contingent upon” might mean. In the minimal sort of relationship between antecedent and consequent, a conditional claim asserts simply that when the antecedent is true the consequent is also true. Basic logical systems use only that minimal relationship. That means it’s possible to accept a conditional statement as true simply when the consequent and antecedent are true as a matter of mere coincidence. For example: “If the Martian moon Phobos is behind the planet Mars, then somewhere on Earth someone is breathing.” Since the location of Phobos has nothing to do with the fact that at this point in time people M O R E TO O L S F O R C R I T I C A L T H I N K I N G A B O U T A R G U M E N T S 23 are always breathing on Earth, this conditional statement is true simply as a matter of coincidence. Of course, the connection between the truth of the antecedent and the truth of the consequent may be stronger. There may even be a causal connection: “If you throw that match into that puddle of gasoline, it will catch fire.” Alternatively, there may also be a kind of logical connection between an antecedent and its consequent: “If something is red, then it has color” or perhaps “If you add 7 to 5, then the result is 12.” There are many relationships that can be captured by a conditional claim. In fact, a rather important relationship for critical thinkers to remember is the one between premises and conclusion. The relationship between the premises and the conclusion of a deductively valid argument may be expressed through a conditional claim, and among logicians a conditional claim is often used to describe this relationship: “If the premises are true, then the conclusion is true.” The relationship here actually has a special name. Valid deductive arguments are conditional claims where the antecedent (the premises) is connected to the consequent (the conclusion) in a particular, logical way called entailment. This issue quickly becomes philosophically complex and contested, but as a matter of common usage, it’s safe to say that one claim or idea entails another when there is a deep, internal, logical, or conceptual connection between them. (See The Philosopher’s Toolkit 4.8, “Entailment/Implication.”) For example, the claim “Bob is a bachelor” entails the claim “Bob is an unmarried man.” A unique and important feature of conditional statements is that they only proceed in one direction. In the conditional statement “If Barack Obama is president, then the United States has a Democratic president,” we know from Barack Obama’s being president that the United States has a Democrat as president. You can’t, however, run the inference in the other direction. We can’t on the basis of this conditional infer from the fact that the president is a Democrat that he is Barack Obama. In “if p, then q,” the truth of q follows from the truth of p, but the truth of p does not follow from the truth of q. (Doing so would be what’s called the fallacy of “affirming the consequent” or an “illicit conversion.” We’ll address that and other errors that arise from not understanding conditionals in 3.4 and 4.5.) Necessary and sufficient conditions Another way to think about the relationship between the antecedent and consequent of a conditional claim is in terms of necessary and sufficient conditions. A necessary condition is a state of affairs that must occur for another state of affairs to occur. For example, the presence of breathable oxygen is a necessary condition for humans to live, which means humans must have breathable oxygen in order to live. Written in terms of “if p, then q,” the claim “Breathable oxygen is a necessary condition for humans to live” becomes “If humans are living, then breathable oxygen is present.” Therefore: The consequent of an “if … then … ” statement is the necessary condition for the antecedent. 24 M O R E TO O L S F O R C R I T I C A L T H I N K I N G A B O U T A R G U M E N T S It is common to put the necessary condition mistakenly in the antecedent of the conditional claim, but thinking about the logic of conditionals can help clear things up. In a conditional statement of the form “if p, then q,” we know that the truth of p is claimed to correlate with the truth of q – that is, a true p is claimed to imply that q is also true. Keeping this in mind and applying it to the claim, “Breathable oxygen is a necessary condition for humans to live,” it should be clear that the presence of breathable oxygen does not result in humans living. Humans need more than just breathable oxygen to live, and so the presence of breathable oxygen alone is not enough to know that humans can live. After all, humans need food, water, and an environment that isn’t too hot or too cold as well. There is, for example, breathable oxygen in a hot pizza oven, but that doesn’t mean humans can live there. So, while breathable oxygen is necessary for humans to live, it is not the only condition that needs to be met for humans to live. Necessary conditions are often indicated by the phrase “only if,” one of the most powerful phrases, logically speaking, in any language. (Note that there are other ways to indicate necessary conditions, too.) It’s quite different for Sammy to say to her children “We’ll go to the movies if you clean your rooms” from “We’ll go to the movies only if you clean your rooms.” In the first instance, there might be other conditions under which the family goes to the movies – perhaps if the kids persuade her, perhaps if a friend calls and asks, perhaps if it snows or rains. In the second instance, however, the phrase “only if ” establishes an exclusive condition that must be met, without which the antecedent won’t be true. The component statement designated by the phrase “only if ” is the necessary condition of a conditional claim. Necessary conditions are powerful claims, because they are very strict in their demands. Although, that’s not the only way to be logically powerful, as we’ll see with another kind of condition. A sufficient condition is a condition that when met is enough to know that some other condition has also been met. More strongly put, its truth (in a true conditional) assures that the consequent is also true. In Sammy’s first sentence (“We’ll go to the movies if you clean your rooms”), the children’s cleaning their rooms is enough to assure them that they’re going to the movies. Sammy’s second formulation, however, the one that makes the children’s cleaning their rooms nothing more than a necessary condition for going to the movies (“We’ll go to the movies only if you clean your rooms.”), does not give the kids a guarantee that if they clean their rooms they’ll go. Meeting a condition stated in the consequent doesn’t guarantee the antecedent, and that’s because it’s merely a necessary and not a sufficient condition. Here’s another example. A blackmailer who says, “I’ll not go to the police with the incriminating information I have about you only if you give me the money,” has not said that giving him the money will result in his not informing the police. In other words, he has not said, strictly speaking, what will happen if the money is paid. The blackmailer has made the much more limited claim that if the money is not paid he will M O R E TO O L S F O R C R I T I C A L T H I N K I N G A B O U T A R G U M E N T S 25 inform the police. Paying the blackmailer is necessary for his not going to the police, but it’s not sufficient to guarantee it. His threat is consistent with his later demanding still more money or with going to the police anyway. That’s one reason blackmail – and cleverly constructed conditionals – can be so maddening. The antecedent of an “if … then … ” statement is the sufficient condition for the consequent. Similarly, the presence of human life in our example is enough to know that there is breathable oxygen present. As a result, the presence of human life is a sufficient condition for the presence of breathable oxygen. Of course, this does not mean that human life somehow causes the presence of breathable oxygen. The relationship between antecedent and consequent in that example is not causal. Again, conditional claims, simply by being conditional claims, do not imply any particular type of relationship between the antecedent and consequent, causal or otherwise – and so neither do statements of necessary and sufficient conditions. Biconditional claims A biconditional claim is a complex claim that expresses a relationship of equivalence between two claims. Two claims are considered equivalent in this logical sense, when they always have the same truth value (that is, they are both true or both false). The claim, “Suzy will get a raise if and only if she gets a promotion,” uses the connective phrase “if and only if ” to denote the biconditional relationship between Suzy’s getting a raise and Suzy’s getting a promotion. When a biconditional is used to connect two claims, it means that one claim will not be true without the other claim also being true – and one claim will not be false without the other claim also being false. In Suzy’s case this means four things: (1) if she gets a raise, then she also gets a promotion, and it means (2) if she gets a promotion, then she also gets a raise. Moreover, (1) if she doesn’t get the promotion, she doesn’t get the raise, and (2) if she doesn’t get the raise, she doesn’t get the promotion. The conjoining of these two conditional claims explains why it is called a “biconditional,” that is “two” conditionals in one claim. Like a conditional claim, the biconditional expresses a relationship of implication between two claims, but unlike a conditional claim, the biconditional’s implication relationship extends to both of the claims composing the biconditional. Written in terms of claims p and q the biconditional “p if and only if q” is the same as saying, “if p, then q and if q, then p,” because not only does p imply q for the biconditional, q also implies p. Logicians commonly abbreviate this “if and only if ” or biconditional relationship with “iff.” In terms of necessary and sufficient conditions, a biconditional claim describes a relationship between two claims such that each individual claim is both necessary and sufficient for the other. For Suzy, this means that getting a raise is both necessary and sufficient for her getting a promotion, and so Suzy can’t have one without the other. She will either get a raise and a promotion, or she will get neither. Claims that are 26 M O R E TO O L S F O R C R I T I C A L T H I N K I N G A B O U T A R G U M E N T S both necessary and sufficient come as a package deal, committing whomever advances those claims to accepting both or neither. Biconditionals are also helpful in critical thinking about concepts, as definitions are often couched as biconditional relationships. For example, a definition of “justice” is a good one if and only if it describes situations that are just or are called “just.” If, therefore, we come across a situation that we accept as just but that doesn’t fit the definition under scrutiny, then that definition must be somehow inadequate. And if we discern a situation that we identify as unjust but that does fit the definition of justice we’re examining, then similarly that definition fails. Philosophers and other critical thinkers often use this strategy to criticize definitions and to clarify concepts. SEE ALSO 4.5 Common Formal Fallacies 6.3 Fallacies about Causation 9.4 Scientific Method READING Michael Woods with David Wiggins, eds., Conditionals (2003) Jonathan Bennett, A Philosophical Guide to the Logic of Conditionals (2003) Julian Baggini & Peter S. Fosl, The Philosopher’s Toolkit (2010) Graham Priest, Logic: A Very Short Introduction (2000) 2.3 Classifying and Comparing Claims When thinking critically, it can be helpful to consider the kinds of claims with which one is dealing, especially the way those sentences relate to truth. Logicians have come up with a number of ways of understanding the truth-bearing qualities of claims and other statements both by (a) comparing them and by (b) categorizing them into types. Comparing claims Here are four of the principal ways logicians compare statements with one another. (Note that some of them overlap.) 1. Consistency. For critical thinking, consistency is one of the most important virtues. So much so, in fact, that those who pride themselves on being good critical thinkers are likely to meet the charge of inconsistency with the utmost indignation. It’s a serious charge. The power of consistency in argumentation has a very long history. Socrates (469–399 bce) in the Platonic dialogues, for example, often ferreted M O R E TO O L S F O R C R I T I C A L T H I N K I N G A B O U T A R G U M E N T S 27 out inconsistency in the remarks of his interlocutors, much to their chagrin. Even in defending his own life in The Apology, Socrates depended on pointing out the inconsistency of his accusers, specifically Meletus. On a far grander scale, in the Book of Job from the Old Testament, Job questions God’s consistency after being allowed to suffer both mental and physical trials for what seemed to Job to be no apparent reason (e.g., Job 10:3). For a devout servant and worshiper of God, Job’s suffering seemed inconsistent with what he knew of God’s character. While it wasn’t an overt accusation of hypocrisy (a logical vice, you might say, when one’s actions are inconsistent with one’s claims about appropriate actions), Job’s remarks were nevertheless an accusation that God did not take lightly. Very roughly speaking, consistency is about things fitting together in a way that makes sense. Both Socrates and Job were wrestling with situations that did not fit together in ways that made sense to them, and they were both very deeply concerned about it. Of course, their concern with inconsistency was partly a function of how it was about to affect or had affected their lives. Nevertheless, their situations may have been more bearable had they not appeared to be the result of obvious inconsistencies. Good critical thinkers, in any case, are adept at recognizing inconsistencies wherever they may appear; and what’s more, they are tenacious about limiting or eliminating them in their own beliefs. In logical terms, consistency is a term used to describe a set of claims that can all be true at the same time. Inconsistency. This occurs within a set of claims when it is not possible for all of the claims to be true at the same time. Maintaining a set of beliefs that is inconsistent means holding onto some beliefs that must, as a matter of logic, be false, which is why a good critical thinker is loath to hold an inconsistent set of beliefs. 2. Contradiction. A contradiction occurs between two claims when the truth of one necessitates the falsity of another, and the falsity of one necessitates the truth of the other. In short, contradictions occur when for logical reasons two claims must have opposite truth values, and so one must always be false while the other is true. Contradictory statements can never have the same truth values at the same time. For example, the claim, “All humans are mortal,” stands in a contradictory relationship with the claim, “Some humans are not mortal.” If “All humans are mortal” is true, then “Some humans are not mortal” must be false. And supposing that “All humans are mortal” is false, then “Some humans are not mortal” must be true. Note that any set of claims containing a contradiction is inconsistent, since it could never be the case that the contradictory claims could be true at the same time. As a result, the set of claims containing a contradiction will always contain at least one falsehood, which is what makes it impossible for all of the claims to be true at the same time. Contradiction, however, is not the only form of inconsistency, as we’ll soon see. 3. Contrariety. Contraries are also inconsistent. Contrariety is a relationship between two claims that occurs when at least one of the claims must be false, and 28 M O R E TO O L S F O R C R I T I C A L T H I N K I N G A B O U T A R G U M E N T S as a result it is impossible for both claims to be true at the same time. In contrast to contradiction, the relationship of contrariety does allow for cases where both claims are false at the same time, since the simple rule of contrariety is just that at least one (and maybe both) of the claims must be false. The claim “Tomorrow is Friday” is contrary to the claim “Tomorrow is Wednesday.” Either of these claims might be true, but at least one of them is false, and both are false, for example, if tomorrow is Thursday. Contrariety, of course, makes creating a consistent set of claims impossible, because at least one of the two claims that are contrary to one another must be false. Therefore, a set containing contrariety will always contain at least one false claim, making it inconsistent. So, both contradictions and contraries yield inconsistent sets of statements. 4. Equivalence. Equivalence describes a relationship between two claims that always have the same truth value. If one claim is true and equivalent to another claim, then the other claim must be true as well. Alternatively, if one of two equivalent claims is false, then the other must be false as well. (The equivalence relationship is, as we saw in 2.2, described by the biconditional.) Common examples of equivalent claims occur when two claims mean the same thing but are expressed in different ways. “Friday is the best day of the week” is equivalent to saying “The day after Thursday is the best day of the week,” since, logically speaking, both claims have the same meaning. Classifying single claims Here are three useful different categories of claims and other statements logicians have identified in terms of their possibilities of bearing truth. 1. Contingent statements. Contingent statements, by far the largest class in natural human languages, are simply statements that can be either true or false. More precisely, they are statements that are possibly true or false. So, the statement, “George W. Bush is president of the United States,” can be either true or false, depending upon what year it is. Note that even while Bush was president, the statement remained a contingent truth. This is so because it was possible for Bush to have lost the election that led to his taking office. For a statement to be contingent all that’s required is that it is possible that in some circumstances it is true and in some other possible circumstances it is false. There must be, as metaphysicians like to say, a logically possible world in which Bush did not win election to the US presidency. If, for example, Gore had won Florida, things would have turned out differently. One easy way, then, to identify a logically contingent statement is to consider whether its negation is a selfcontradiction. No contingent statements have negations that are self-contradictory, because it’s logically possible for every contingent statement to possess the opposite truth value from the one it happens to have. Self-contradictions don’t work that way. 2. Self-contradictions. Self-contradictions are different from contingent statements because under all possible circumstances they always possess the same truth M O R E TO O L S F O R C R I T I C A L T H I N K I N G A B O U T A R G U M E N T S 29 value – false. Self-contradictions are also always equivalent to one another, of course, because they have the same truth value. It follows from this, if you think about it, that while all self-contradictions are equivalent, none are consistent. In fact, none are consistent with any other statement. That’s because, obviously, there can never be a set of self-contradictions or set containing even a single self-contradiction of which all are true – which is what the definition of consistency requires. “This year is 2016, and this year is not 2016” is an example of a self-contradictory statement since no matter what year it is the sentence is false. A typical form of self-contradiction is “p and not-p.” 3. Tautologies. There’s another class of sentences, tautologies, which like selfcontradictions always have the same truth value in all possible worlds and, moreover, are always equivalent to one another. In the case of tautologies, however, that’s because they’re always true. In this sense, tautologies are just the opposite of selfcontradictions. “This year is 2016, or this year is not 2016,” is an example of a tautology, since no matter what year it is the sentence is true. A common form of tautology is “p or not-p.” SEE ALSO 3.4 4.3 9.5 Formal Deduction with Categories: Immediate Inferences Equivalences Unfalsifiability and Falsification Resistance READING David Kelley, The Art of Reasoning, 3rd edn (2013) Deborah J. Bennett, Logic Made Easy (2004) M. J. Cresswell & G. E. Hughes, A New Introduction to Modal Logic (1996) 2.4 Claims and Definitions Some words and ideas seem pretty easy to define. A bachelor is an unmarried man, for example. Some seem a bit harder. A square is a two-dimensional, equilateral, closed, four-sided rectangle. Still others seem all but impossible to define, perhaps because definitions in those cases are in fact impossible. How would you define goodness, or beauty, or justice, or being? Critical thinking, however, often depends upon a sensitivity to the meanings of words and therefore to matters of definition. Claims, as we’ve discussed, are assertions about what is true or false, but claims would be vacuous if the words that composed them didn’t have specific meanings. If you think of all the words you’ve acquired as books filling the library of your mind, then definitions function like rules for organizing that library by bringing precision and clarity to the concepts 30 M O R E TO O L S F O R C R I T I C A L T H I N K I N G A B O U T A R G U M E N T S related to each word. Definitions tell us what bits of information belong together, and how categories of information relate to one another. Lexical, stipulative, ostensive, and negative definition Dictionaries are, of course, relatively good resources for anyone interested in finding out what a word means. Using one set of words to define another word is called a lexical definition. But it’s important to understand the limits of dictionary definitions. More often than not, a definition in a dictionary requires readers to have a fairly robust understanding of the language already at their disposal. In other words, a dictionary functions in many cases as a cross-reference or translator between words one knows and words that one doesn’t yet know. Even the most obscure words in a dictionary, say, for example, “pulchritudinous” or “kalokagathia,” must be defined using words that the reader already knows and understands. Otherwise, the dictionary isn’t very helpful. Another potential problem with dictionaries is that they often simply report on the way a word is commonly used, which can nevertheless be conceptually problematic and can change significantly over time. Critical thinkers and other inquirers, in contrast, are often interested in more precise, more accurate, and often more enduring definitions; and so sometimes a new or more precise meaning for a term is simply stipulated in what’s called, obviously enough, a stipulative definition. The word “friend,” for example, is used in many ways and many contexts, but the question as to what is the best definition of “friend” may require moving beyond common usage to a more critical analysis of the concept. Similarly, the word “valid” is often used to describe claims made in common parlance (“You make a valid point.”). But as we’ve discussed in 2.1, the word “valid” in logic has a very specific meaning and applies only to arguments; it does not apply to claims or points. Becoming a good critical thinker, then, requires distinguishing how words are commonly used from the way they are used in more precise contexts. Sometimes, however, things get even more complex. There seem to be words that may be defined not through other words but only by pointing to something in our experience, through what’s called ostensive definition. “Red,” for example, may be impossible to define without somehow pointing to an instance of red. Individual things may be impossible to define, too, as individuals – though it’s certainly possible to describe them or name them. Could anyone perfectly define you? In addition, there are negative definitions. While it’s generally a poor practice to define things negatively, by what they are not rather than by what they are, the medieval Andalusian Jewish philosopher Maimonides (c. 1135–1204) thought that humans could understand God only by articulating what God is not. Positively speaking, according to Maimonides, the human mind just can’t apprehend God. Extension and intension The extensional meaning of a concept is just the set of things objectively picked out by the concept. So, the extension of the concept “dog” would be all those things in M O R E TO O L S F O R C R I T I C A L T H I N K I N G A B O U T A R G U M E N T S 31 the world that are properly picked out by that concept. Refining the definition (as well as the concept of “dog”) expands or contracts that extension. Should it include coyotes? Wolves? Hyenas? A good definition should get the extension of a concept just right, not casting it too broadly or too narrowly. It does that by articulating criteria for including or excluding candidates from the term or concept’s extension, or from the class or category it designates. We might call devices for determining what is properly included or excluded from a class or group or category criteria for class membership. A related idea is denotation. What a term denotes is its most literal, direct, or apparent meaning. By contrast, the connotation of a word, or what it connotes, are meanings that are oblique, more figurative, and associated less obviously with it. The intensional meaning of the concept, by contrast, is just what people think or believe or otherwise subjectively take a concept to mean or refer to. In the past, people meant something different by the terms “morning star” and “evening star” in an intensional sense, even though the extension of those terms turned out to be one and the same object – namely, the planet Venus. Good critical thinkers, therefore, should aspire to having the definitions of the substantive terms they use match as closely as possible their true extension. (We know that this can get complicated, but be patient. Its importance will become clearer once we get to Chapters 3 and 4. For a bit of background on this topic, see The Philosopher’s Toolkit entry, “Sense and Reference.”) Generic similarities and specific differences Definitions often accomplish their task of setting the proper boundaries among concepts and tailoring terms to their proper extension by situating them among broader but interlocking, containing terms. So, for example, Aristotelians commonly defined human beings as rational animals. “Animal” is a broader term than human, and often called the genus term in a definition. “Rational” here establishes what’s commonly called the “specific difference” or differentia, which indicates what essentially or distinctively sets off humans from other animals. (Of course, this definition of human being has for a long time been rather successfully challenged, but you get the point.) Biologists define organisms in a similar way using a strategy that runs all the way back to Aristotle’s Categories – that is, by nesting them in an extensive series of increasingly general concepts: kingdom, phylum, class, order, family, genus, and finally species.1 Now, that’s probably a more precise definition than needed for most purposes, but it does exemplify how situating a term or concept among what is more general and more specific, that is, among its similarities and differences in